About GeometricCalculator.org

Most geometry calculators make you pick a formula first: “area from radius”, “radius from circumference”… This site works the other way round. Each shape is described once, as a set of measurements and the relationships between them. Enter whatever you happen to know and the solver figures out the rest.

How the solver works

First it chains together exact formulas, the same ones in your textbook, so the step-by-step working is the working you would write by hand. When a formula has two valid answers (an arcsine, a square root with ±), the solver follows both branches and discards the ones that break the shape’s rules, which is how the ambiguous triangle case is handled.

Some combinations have no closed-form answer at all, a cylinder from its volume and total surface area, a triangle from its perimeter and two heights. For those, the solver switches to a numerical method (Levenberg–Marquardt from many starting points), verifies every candidate against all the shape’s formulas, and reports each distinct solution it finds.

Special functions are computed exactly rather than approximated: the ellipse perimeter uses the arithmetic–geometric mean and the ellipsoid surface area uses Carlson’s elliptic integrals.

Accuracy

All arithmetic is IEEE double precision (about 15–16 significant digits). The formulas are tested automatically: for every shape, every combination of inputs is fed back into the solver and must reproduce the original shape.

Privacy

All calculations happen in your browser. Nothing you type is sent anywhere. See the privacy page.